A015579 Expansion of g.f. x/(1 - 9*x - 2*x^2).

0, 1, 9, 83, 765, 7051, 64989, 599003, 5521005, 50887051, 469025469, 4323003323, 39845080845, 367251734251, 3384955769949, 31199105398043, 287561860122285, 2650454951896651, 24429218287314429, 225163874489623163, 2075333306981237325, 19128327511810382251

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,2).

Formula

a(n) = 9*a(n-1) + 2*a(n-2).

E.g.f.: 2*exp(9*x/2)*sinh(sqrt(89)*x/2)/sqrt(89). - Stefano Spezia, Apr 06 2023

Mathematica

Join[{a=0, b=1}, Table[c=9*b+2*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)
LinearRecurrence[{9, 2}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)
CoefficientList[Series[x/(1-9x-2x^2), {x, 0, 30}], x] (* Harvey P. Dale, Aug 14 2023 *)

Prog

(Sage) [lucas_number1(n, 9, -2) for n in range(0, 19)] # Zerinvary Lajos, Apr 26 2009
(Magma) [n le 2 select n-1 else 9*Self(n-1) + 2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-9*x-2*x^2))) \\ G. C. Greubel, Jan 06 2018

Crossrefs

Cf. A099371.

Sequence in context: A048353 A037502 A037679 * A162759 A147960 A155499

Adjacent sequences: A015576 A015577 A015578 * A015580 A015581 A015582

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

Extended by T. D. Noe, May 23 2011

Status

approved